1. M / M / 1 / GD / / (Section 4) Little’s queuing formula This is independent of number of servers, queue discipline, interarrival time dist., service time dist. IE 417, Chap 22, April 99 Steady-state condition:

2. Burger-417 Fast-Food = 45 #/hr = 0.75 #/min = 60 #/hr = 1 #/min Based on solution on web. 1 teller1 teller & cashier 2 tellers = 1 = 1.25 = 1 L q # 2.250.90.12 L # 31.50.87 W q min 31.20.16 W min 421.16 0.750.60.38 0.250.40.45 P w 0.750.60.20 P(j 5) 0.240.080.01 1 IE 417, Chap 22, May 99

3. Different Types of Costs in Queuing Systems ($/part)Loss in goodwill = C Waiting time = ($/unit time) Loss of customer = ($/part) IE 417, Chap 22, April 99 Cost of space = ($/part) Lq

4. M / M / 1 / GD / C / (Section 5) For j = 1, …., C For j = 0, …., C For j = C+1, …., IE 417, Chap 22, May 99

5. M / M / S / GD / / (Section 6) IE 417, Chap 22, May 99 Steady-state condition: For j = 1, 2, …, SFor j = S+1, S+2, …, Probability that an arriving unit has to wait: Table 6 page 1088

6. M / M / S / GD / / (Section 6) Cont. IE 417, Chap 22, May 99